In a medium heavy bottomed saucepan, combine milk, rice and salt and bring to a boil over high heat. Reduce heat to low and simmer until the rice is tender, about 20 minutes. Stir frequently to prevent the rice from sticking to the bottom of the pan.
In a small mixing bowl, whisk together egg and sugar until well mixed. Add a half cup of the rice mixture – a tablespoon at a time – beating to incorporate.
Add egg mixture back into the saucepan of rice and milk and stir, on low heat, for 10 minutes or so, until thickened. Be careful not to have the mixture come to a boil at this point. Stir in the vanilla. Remove from heat and stir in the cinnamon.
Serve warm or cold.
I sometimes add 1/2-3/4 golden raisins while the rice is cooking, they will plump up and be delicous.